Problem: Multiply.
$12 \times 81$ and $0.12 \times 8.1$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $12 \times 81$. Then we can estimate to place the decimal point in the product of $0.12 \times 8.1$. $\begin{aligned} 81&\\ \underline{ \times 12}&\\ 2}\\ 160}\\ 10}\\ \underline{+800}}\\ 972 \end{aligned}$ Let's estimate to place the decimal in $0.12 \times 8.1$. $\begin{aligned} 0.12 \times 8.1 &\approx 0.1 \times 8\\\\ &\approx \dfrac{1}{10}\times \dfrac{8}{1}\\\\ &\approx \dfrac{8}{10}\\\\ &\approx 0.8 \end{aligned}$ Where can we place the decimal in $972$ to get a product close to $0.8$ ? $0.972 = 0.12 \times 8.1$